Rotor Free‐Wake Modeling Using a Pseudo‐Implicit Technique — Including Comparisons with Experimental Data

Bagai, Ashish; Leishman, J. Gordon

doi:10.4050/jahs.40.29

Cited by 158 publications

(69 citation statements)

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“…The additional aerodynamic loads caused by trailing-edge flap motion are calculated using a time domain unsteady aerodynamic model proposed by Hariharan and Leishman [37]. A free-wake model is used to determine the induced inflow distribution over the rotor disk [38]. Further details about the aerodynamic modeling are available in [21].…”

Section: B Aerodynamic Modelmentioning

confidence: 99%

Optimal Placement of Piezoelectric Actuated Trailing-Edge Flaps for Helicopter Vibration Control

Viswamurthy

Ganguli

2009

Journal of Aircraft

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This study aims to determine the optimal locations for dual trailing-edge flaps on a helicopter blade in the presence of actuator hysteresis. An aeroelastic analysis based on a finite element approach in space and time is used in conjunction with an optimal control algorithm to determine the actuator control input for vibration minimization. The reduced hub-vibration level and the flap power are the two optimization indices considered in this study. The location of the flaps along the blade are the design variables. The hysteresis in the piezo-actuators is modeled using a dynamic hysteresis model based on an extension to the classical Preisach model. It is found that second-order polynomial response surfaces based on the central composite design of the theory of design of experiments describe both objectives adequately. Numerical studies for a four-bladed hingeless rotor show that both objectives are more sensitive to outboard flap location compared with inboard flap location. Optimization studies indicate that the dualflap configuration for the least hub-vibration level is different from the configuration for the least flap power. The Pareto front between the two objectives is found to be discontinuous. However, a reasonable tradeoff configuration is obtained by careful inspection of the Pareto front. This configuration yields about a 70% reduction in hub-vibration levels from the baseline conditions at an advance ratio of 0.30, while requiring about 21% more flap power from the initial configuration of the optimization study. Nomenclature C T = rotor thrust coefficient c = blade chord c f = trailing-edge flap chord EI y = flap bending stiffness EI z = lag bending stiffness F x = vibratory hub longitudinal shear force F y = vibratory hub lateral shear force F z = vibratory hub vertical shear force GJ = torsion stiffness J = objective function M h = trailing-edge flap hinge moment M x = vibratory hub roll moment M y = vibratory hub pitch moment M z = vibratory hub yaw moment m f = trailing-edge flap mass per unit length m 0 = blade mass per unit length P f = power required by a single trailing-edge flap, averaged over one revolution P t = total actuation power required by all flaps on all rotor blades, averaged over one revolution R = rotor radius u = input to the hysteresis transducer/voltage applied to the piezostack, V X f g = trailing-edge flap center of gravity (after hinge) x 1 , x 2 = nondimensional location of the inboard and outboard flap, respectively = output of the hysteresis transducer/flap deflection angle, deg = hysteresis operator = lock number = advance ratio/Preisach distribution function 0 , 1 , 2 = Preisach distribution functions for the dynamic hysteresis model = blade solidity ratio = blade azimuth angle = rotor angular speed Subscripts St = steady component Nc = Nth cosine harmonic Ns = Nth sine harmonic Superscript 4p = 4/rev component

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Section: B Aerodynamic Modelmentioning

confidence: 99%

Optimal Placement of Piezoelectric Actuated Trailing-Edge Flaps for Helicopter Vibration Control

Viswamurthy

Ganguli

2009

Journal of Aircraft

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“…In the present analysis, a five-point difference scheme 13 with equal difference steps, that is, ψ = ζ , was used. A predictioncorrection-relaxation scheme improved over Ref.…”

Section: Free Wake Modelmentioning

confidence: 99%

New Hybrid Method for Predicting the Flowfields of Helicopter Rotors

Zhao

2006

Journal of Aircraft

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Based on a Navier-Stokes/full potential/free wake solver, a new hybrid method was developed for efficient predictions of the three-dimensional viscous flowfield of a helicopter rotor under both hover and forward flight conditions. The developed flow solver was composed of three modules: 1) a compressible Navier-Stokes analysis to model the viscous flow and near wake about the blade, 2) a compressible potential flow analysis to model the inviscid isentropic potential flow region far away from the rotor, and 3) a free wake model to account for tip vortex effects once the tip vortex leaves the viscous flow region and enters the potential flow region. In this hybrid method, a moving embedded grid methodology was adopted that accounts for rigid blade motions in rotation, flapping, and pitching. A dual-time method was employed to fulfill the calculation of the unsteady flowfields of helicopter rotors, and a third-order upwind scheme (MUSCL) and flux-difference splitting scheme without introducing artificial viscosity were used to calculate the flux. To search suitable donor elements in embedded grids to pass information between the viscous flow and potential flow zones, a new searching scheme was implemented. The sectional pressure distributions of a UH-60A helicopter rotor and an AH-1G model rotor in hover and forward flight, with and without the wake model, were calculated, and the developed hybrid model was validated by comparing with available experimental data. The simulated steady and unsteady lifting results of a model rotor with three different blade-tip planforms demonstrate the benefits of the curvilinear swept tip and constant swept tip in suppressing supercritical flows. NomenclatureA 1 = lateral cyclic pitch angle a 0 = cone angle a 1s = longitudinal tip-path-plane tilt angle B 1 = longitudinal cyclic pitch angle b 1s = lateral tip-path-plane tilt angle C L = section lift coefficient (u, v, w) = velocity vector in Cartesian coordinate systemgrid velocity vector in Cartesian coordinate system q ∞ = freestream velocity R(ψ, ζ ) = location vector of a collocation point on vortex filament r/R = radial blade station nondimensionalized by rotor radius S = surface of the control cell .cn. ‡ Ph.D. Student. T = absolute temperature t = physical time V = control cell volume W = vector of conserved flow variables x, y, z = Cartesian coordinate system β(t) = flapping angle = circulation of vortex + = forward difference operator − = backward difference operator ζ = wake age θ(t) = blade pitch angle θ 0 = collective pitch angle μ = advance ratio ρ = air density τ = pseudo time φ = velocity potential ψ(t) = azimuth angle = rotor rotational speed ω R = relaxation factor Subscripts i, j, k = grid indices n = local surface normal vector ∞ = undisturbed flow

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“…An analysis based on a pseudo-implicit, predictor-corrector (PIPC) relaxation algorithm, (Refs. [34][35][36] has been developed to integrate Eq. 4.…”

Section: Collocation Pointsmentioning

confidence: 99%

Accelerated, high resolution free-vortex wakes for rotor aeroacoustic analysis

Bagai

Leishman

Glenn³

1997

15th Applied Aerodynamics Conference

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Numerical acceleration algorithms have been developed to improve the computational efficiency of rotor free-vortex wake analyses. Two general methodologies were formulated: an adaptive grid sequencing algorithm, and a velocity field interpolation algorithm. The methods were found to produce up to an order of magnitude decrease in execution time, but without significant loss in predictive accuracy. Examples are shown for very high fidelity wake geometries required for rotor aeroacoustic analyses.

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Rotor Free‐Wake Modeling Using a Pseudo‐Implicit Technique — Including Comparisons with Experimental Data

Cited by 158 publications

References 0 publications

Optimal Placement of Piezoelectric Actuated Trailing-Edge Flaps for Helicopter Vibration Control

Optimal Placement of Piezoelectric Actuated Trailing-Edge Flaps for Helicopter Vibration Control

New Hybrid Method for Predicting the Flowfields of Helicopter Rotors

Accelerated, high resolution free-vortex wakes for rotor aeroacoustic analysis

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